In this paper, we consider the problem of generating inspection paths for robots. These paths should allow an attached measurement device to perform high-quality measurements. We formally show that generating robot paths, while maximizing the inspection quality, naturally corresponds to the submodular orienteering problem. Traditional methods that are able to generate solutions with mathematical guarantees do not scale to real-world problems. In this work, we propose a method that is able to generate near-optimal solutions for real-world complex problems. We experimentally test this method in a wide variety of inspection problems and show that it nearly always outperforms traditional methods. We furthermore show that the near-optimality of our approach makes it more robust to changing the inspection problem, and is thus more general.